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1 solution
First thing you need to know is that period is independent of amplitude. What matters in the case of this question is the absolute value notation at either end of the trig. It is common knowledge that the period of a sin function is 2π, but when it's the absolute value of the trig, the part of the graph that is below the 0 is mirrored or becomes positive. Thus, the entire function begins repeating itself on every half cycle, so π.